df <- as_tibble(read.table("winequality-red.csv", sep=";", header = TRUE))
df_white <- as_tibble(read.table("winequality-white.csv", sep=";", header = TRUE))
index = sample(1:nrow(df), 0.7*nrow(df))
train = df[index,] # Create the training data
test = df[-index,] # Create the test data
dim(train)
## [1] 1119 12
dim(test)
## [1] 480 12
lm_basic <- lm(data = df, quality ~ .)
summary(lm_basic)
##
## Call:
## lm(formula = quality ~ ., data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.68911 -0.36652 -0.04699 0.45202 2.02498
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.197e+01 2.119e+01 1.036 0.3002
## fixed.acidity 2.499e-02 2.595e-02 0.963 0.3357
## volatile.acidity -1.084e+00 1.211e-01 -8.948 < 2e-16 ***
## citric.acid -1.826e-01 1.472e-01 -1.240 0.2150
## residual.sugar 1.633e-02 1.500e-02 1.089 0.2765
## chlorides -1.874e+00 4.193e-01 -4.470 8.37e-06 ***
## free.sulfur.dioxide 4.361e-03 2.171e-03 2.009 0.0447 *
## total.sulfur.dioxide -3.265e-03 7.287e-04 -4.480 8.00e-06 ***
## density -1.788e+01 2.163e+01 -0.827 0.4086
## pH -4.137e-01 1.916e-01 -2.159 0.0310 *
## sulphates 9.163e-01 1.143e-01 8.014 2.13e-15 ***
## alcohol 2.762e-01 2.648e-02 10.429 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.648 on 1587 degrees of freedom
## Multiple R-squared: 0.3606, Adjusted R-squared: 0.3561
## F-statistic: 81.35 on 11 and 1587 DF, p-value: < 2.2e-16
Volatile acidity, chlorides, total sulfur dioxide, sulphates and alcohol are all very statistically significant, although our adjusted \(R^2\) is still quite low.
train_control <- trainControl(method = "cv", number = 5)
model_ridge <- train(quality ~ .,
data = df,
method = "ridge", # method
trControl = train_control) # cross validation
model_ridge
## Ridge Regression
##
## 1599 samples
## 11 predictor
##
## No pre-processing
## Resampling: Cross-Validated (5 fold)
## Summary of sample sizes: 1280, 1280, 1279, 1279, 1278
## Resampling results across tuning parameters:
##
## lambda RMSE Rsquared MAE
## 0e+00 0.6522813 0.3490324 0.5055778
## 1e-04 0.6522800 0.3490349 0.5055761
## 1e-01 0.6522864 0.3494269 0.5046582
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was lambda = 1e-04.
#something doesn't seem to be working here
model_stepwise <- train(quality ~ .,
data = df,
method = "glmStepAIC",
trControl = train_control)
## Start: AIC=2545.06
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 537.24 2543.3
## - fixed.acidity 1 537.45 2543.8
## - residual.sugar 1 537.64 2544.2
## <none> 537.15 2545.1
## - free.sulfur.dioxide 1 538.42 2546.1
## - citric.acid 1 538.73 2546.8
## - pH 1 539.50 2548.6
## - chlorides 1 544.44 2560.3
## - total.sulfur.dioxide 1 544.72 2560.9
## - sulphates 1 560.75 2598.0
## - volatile.acidity 1 568.08 2614.6
## - alcohol 1 575.99 2632.3
##
## Step: AIC=2543.27
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 537.49 2541.9
## - residual.sugar 1 537.66 2542.3
## <none> 537.24 2543.3
## - free.sulfur.dioxide 1 538.57 2544.4
## - citric.acid 1 538.84 2545.1
## - pH 1 541.51 2551.4
## - chlorides 1 544.73 2559.0
## - total.sulfur.dioxide 1 544.99 2559.6
## - sulphates 1 561.62 2598.0
## - volatile.acidity 1 569.07 2614.8
## - alcohol 1 635.19 2755.3
##
## Step: AIC=2541.87
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 537.96 2541.0
## <none> 537.49 2541.9
## - citric.acid 1 538.90 2543.2
## - free.sulfur.dioxide 1 538.94 2543.3
## - pH 1 544.82 2557.2
## - chlorides 1 546.51 2561.1
## - total.sulfur.dioxide 1 546.75 2561.7
## - sulphates 1 562.40 2597.8
## - volatile.acidity 1 570.03 2615.0
## - alcohol 1 635.77 2754.5
##
## Step: AIC=2540.99
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 537.96 2541.0
## - citric.acid 1 539.16 2541.8
## - free.sulfur.dioxide 1 539.68 2543.1
## - pH 1 545.36 2556.5
## - chlorides 1 546.82 2559.9
## - total.sulfur.dioxide 1 547.01 2560.3
## - sulphates 1 562.50 2596.0
## - volatile.acidity 1 570.04 2613.0
## - alcohol 1 638.05 2757.1
## Start: AIC=2556.61
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 541.62 2554.6
## - fixed.acidity 1 541.65 2554.7
## - residual.sugar 1 541.70 2554.8
## - density 1 541.73 2554.9
## <none> 541.61 2556.6
## - free.sulfur.dioxide 1 543.33 2558.7
## - pH 1 544.00 2560.2
## - chlorides 1 547.55 2568.6
## - total.sulfur.dioxide 1 548.78 2571.4
## - sulphates 1 563.77 2605.9
## - volatile.acidity 1 566.03 2611.0
## - alcohol 1 576.37 2634.2
##
## Step: AIC=2554.63
## .outcome ~ fixed.acidity + volatile.acidity + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 541.68 2552.8
## - residual.sugar 1 541.71 2552.9
## - density 1 541.74 2552.9
## <none> 541.62 2554.6
## - free.sulfur.dioxide 1 543.34 2556.7
## - pH 1 544.03 2558.3
## - chlorides 1 547.86 2567.3
## - total.sulfur.dioxide 1 549.14 2570.3
## - sulphates 1 563.80 2604.0
## - volatile.acidity 1 575.66 2630.6
## - alcohol 1 577.73 2635.2
##
## Step: AIC=2552.77
## .outcome ~ volatile.acidity + residual.sugar + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 541.73 2550.9
## - density 1 541.74 2550.9
## <none> 541.68 2552.8
## - free.sulfur.dioxide 1 543.46 2555.0
## - chlorides 1 548.21 2566.1
## - pH 1 549.20 2568.4
## - total.sulfur.dioxide 1 549.65 2569.5
## - sulphates 1 564.09 2602.6
## - volatile.acidity 1 577.22 2632.1
## - alcohol 1 604.74 2691.6
##
## Step: AIC=2550.89
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 541.75 2549.0
## <none> 541.73 2550.9
## - free.sulfur.dioxide 1 543.60 2553.3
## - chlorides 1 548.21 2564.1
## - pH 1 549.23 2566.5
## - total.sulfur.dioxide 1 549.69 2567.6
## - sulphates 1 564.36 2601.2
## - volatile.acidity 1 577.25 2630.1
## - alcohol 1 615.84 2712.9
##
## Step: AIC=2548.96
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 541.75 2549.0
## - free.sulfur.dioxide 1 543.63 2551.4
## - chlorides 1 548.24 2562.2
## - pH 1 549.52 2565.2
## - total.sulfur.dioxide 1 549.69 2565.6
## - sulphates 1 564.84 2600.3
## - volatile.acidity 1 577.34 2628.3
## - alcohol 1 640.10 2760.3
## Start: AIC=2543.52
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 536.50 2541.5
## - residual.sugar 1 536.50 2541.5
## - fixed.acidity 1 536.68 2541.9
## <none> 536.50 2543.5
## - citric.acid 1 537.57 2544.1
## - pH 1 538.00 2545.1
## - free.sulfur.dioxide 1 538.87 2547.2
## - chlorides 1 543.90 2559.0
## - total.sulfur.dioxide 1 544.95 2561.5
## - sulphates 1 555.38 2585.7
## - volatile.acidity 1 569.42 2617.6
## - alcohol 1 577.06 2634.7
##
## Step: AIC=2541.52
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 536.51 2539.5
## - fixed.acidity 1 537.05 2540.8
## <none> 536.50 2541.5
## - citric.acid 1 537.57 2542.1
## - pH 1 538.66 2544.7
## - free.sulfur.dioxide 1 538.88 2545.2
## - chlorides 1 543.97 2557.2
## - total.sulfur.dioxide 1 545.02 2559.7
## - sulphates 1 556.72 2586.8
## - volatile.acidity 1 569.77 2616.4
## - alcohol 1 629.32 2743.4
##
## Step: AIC=2539.54
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + chlorides +
## free.sulfur.dioxide + total.sulfur.dioxide + pH + sulphates +
## alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 537.07 2538.9
## <none> 536.51 2539.5
## - citric.acid 1 537.57 2540.1
## - pH 1 538.67 2542.7
## - free.sulfur.dioxide 1 538.95 2543.3
## - chlorides 1 543.98 2555.2
## - total.sulfur.dioxide 1 545.04 2557.7
## - sulphates 1 556.76 2584.9
## - volatile.acidity 1 569.84 2614.6
## - alcohol 1 630.30 2743.4
##
## Step: AIC=2538.88
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 537.61 2538.2
## <none> 537.07 2538.9
## - free.sulfur.dioxide 1 539.67 2543.1
## - pH 1 542.11 2548.8
## - chlorides 1 546.01 2558.0
## - total.sulfur.dioxide 1 547.35 2561.1
## - sulphates 1 557.68 2585.0
## - volatile.acidity 1 570.45 2613.9
## - alcohol 1 630.35 2741.6
##
## Step: AIC=2538.17
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 537.61 2538.2
## - free.sulfur.dioxide 1 540.62 2543.3
## - pH 1 542.22 2547.1
## - chlorides 1 547.29 2559.0
## - total.sulfur.dioxide 1 548.94 2562.8
## - sulphates 1 557.80 2583.3
## - volatile.acidity 1 575.73 2623.7
## - alcohol 1 631.71 2742.3
## Start: AIC=2542.23
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 534.93 2540.7
## - pH 1 535.31 2541.6
## - residual.sugar 1 535.49 2542.0
## <none> 534.75 2542.2
## - density 1 535.60 2542.3
## - fixed.acidity 1 535.61 2542.3
## - free.sulfur.dioxide 1 536.09 2543.5
## - total.sulfur.dioxide 1 540.99 2555.1
## - chlorides 1 541.04 2555.2
## - volatile.acidity 1 554.52 2586.8
## - sulphates 1 554.72 2587.2
## - alcohol 1 566.09 2613.2
##
## Step: AIC=2540.68
## .outcome ~ fixed.acidity + volatile.acidity + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - pH 1 535.46 2539.9
## - residual.sugar 1 535.63 2540.3
## - fixed.acidity 1 535.63 2540.4
## <none> 534.93 2540.7
## - density 1 535.80 2540.8
## - free.sulfur.dioxide 1 536.48 2542.4
## - total.sulfur.dioxide 1 542.31 2556.2
## - chlorides 1 542.45 2556.6
## - sulphates 1 554.88 2585.6
## - volatile.acidity 1 559.93 2597.2
## - alcohol 1 566.22 2611.5
##
## Step: AIC=2539.94
## .outcome ~ fixed.acidity + volatile.acidity + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + sulphates + alcohol
##
## Df Deviance AIC
## <none> 535.46 2539.9
## - residual.sugar 1 536.75 2541.0
## - free.sulfur.dioxide 1 536.81 2541.2
## - density 1 538.20 2544.5
## - fixed.acidity 1 540.40 2549.7
## - total.sulfur.dioxide 1 542.35 2554.3
## - chlorides 1 542.45 2554.6
## - sulphates 1 556.73 2587.8
## - volatile.acidity 1 560.68 2596.9
## - alcohol 1 572.70 2624.1
## Start: AIC=2480.66
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - free.sulfur.dioxide 1 510.51 2479.9
## - fixed.acidity 1 510.54 2480.0
## <none> 510.02 2480.7
## - density 1 510.85 2480.8
## - citric.acid 1 511.01 2481.2
## - pH 1 511.33 2482.0
## - residual.sugar 1 511.66 2482.8
## - total.sulfur.dioxide 1 514.79 2490.6
## - chlorides 1 516.37 2494.5
## - sulphates 1 533.92 2537.3
## - volatile.acidity 1 537.34 2545.5
## - alcohol 1 546.67 2567.5
##
## Step: AIC=2479.9
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + total.sulfur.dioxide + density + pH + sulphates +
## alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 511.17 2479.5
## <none> 510.51 2479.9
## - density 1 511.48 2480.3
## - pH 1 511.63 2480.7
## - citric.acid 1 511.81 2481.2
## - residual.sugar 1 512.48 2482.8
## - total.sulfur.dioxide 1 515.81 2491.1
## - chlorides 1 516.65 2493.2
## - sulphates 1 534.95 2537.8
## - volatile.acidity 1 540.02 2549.8
## - alcohol 1 546.91 2566.1
##
## Step: AIC=2479.54
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + total.sulfur.dioxide + density + pH + sulphates +
## alcohol
##
## Df Deviance AIC
## - density 1 511.48 2478.3
## <none> 511.17 2479.5
## - citric.acid 1 512.02 2479.7
## - residual.sugar 1 512.54 2481.0
## - pH 1 516.79 2491.5
## - total.sulfur.dioxide 1 517.55 2493.4
## - chlorides 1 518.70 2496.3
## - sulphates 1 534.99 2535.8
## - volatile.acidity 1 540.33 2548.6
## - alcohol 1 570.89 2619.0
##
## Step: AIC=2478.34
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 511.48 2478.3
## - residual.sugar 1 512.54 2479.0
## - citric.acid 1 513.21 2480.7
## - pH 1 517.11 2490.3
## - total.sulfur.dioxide 1 517.55 2491.4
## - chlorides 1 518.72 2494.3
## - sulphates 1 535.26 2534.5
## - volatile.acidity 1 544.56 2556.6
## - alcohol 1 618.45 2719.4
## Start: AIC=3164.28
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## density + pH + sulphates + alcohol
##
## Df Deviance AIC
## - density 1 666.70 3163.0
## - fixed.acidity 1 666.80 3163.2
## - residual.sugar 1 666.91 3163.5
## - citric.acid 1 667.06 3163.8
## <none> 666.41 3164.3
## - free.sulfur.dioxide 1 668.10 3166.3
## - pH 1 668.37 3167.0
## - chlorides 1 674.80 3182.3
## - total.sulfur.dioxide 1 674.84 3182.4
## - sulphates 1 693.38 3225.7
## - volatile.acidity 1 700.03 3241.0
## - alcohol 1 712.08 3268.3
##
## Step: AIC=3162.96
## .outcome ~ fixed.acidity + volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - fixed.acidity 1 666.81 3161.2
## - residual.sugar 1 666.93 3161.5
## - citric.acid 1 667.35 3162.5
## <none> 666.70 3163.0
## - free.sulfur.dioxide 1 668.53 3165.3
## - pH 1 671.02 3171.3
## - total.sulfur.dioxide 1 675.43 3181.8
## - chlorides 1 675.46 3181.8
## - sulphates 1 693.98 3225.1
## - volatile.acidity 1 701.70 3242.8
## - alcohol 1 786.37 3424.9
##
## Step: AIC=3161.22
## .outcome ~ volatile.acidity + citric.acid + residual.sugar +
## chlorides + free.sulfur.dioxide + total.sulfur.dioxide +
## pH + sulphates + alcohol
##
## Df Deviance AIC
## - residual.sugar 1 667.06 3159.8
## - citric.acid 1 667.37 3160.6
## <none> 666.81 3161.2
## - free.sulfur.dioxide 1 668.71 3163.8
## - pH 1 673.87 3176.1
## - chlorides 1 676.75 3182.9
## - total.sulfur.dioxide 1 676.84 3183.1
## - sulphates 1 694.48 3224.2
## - volatile.acidity 1 703.04 3243.8
## - alcohol 1 787.44 3425.1
##
## Step: AIC=3159.84
## .outcome ~ volatile.acidity + citric.acid + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## - citric.acid 1 667.54 3159.0
## <none> 667.06 3159.8
## - free.sulfur.dioxide 1 669.13 3162.8
## - pH 1 674.20 3174.9
## - total.sulfur.dioxide 1 676.89 3181.2
## - chlorides 1 676.89 3181.2
## - sulphates 1 694.51 3222.3
## - volatile.acidity 1 703.04 3241.8
## - alcohol 1 789.73 3427.8
##
## Step: AIC=3158.98
## .outcome ~ volatile.acidity + chlorides + free.sulfur.dioxide +
## total.sulfur.dioxide + pH + sulphates + alcohol
##
## Df Deviance AIC
## <none> 667.54 3159.0
## - free.sulfur.dioxide 1 669.93 3162.7
## - pH 1 674.61 3173.8
## - total.sulfur.dioxide 1 678.32 3182.6
## - chlorides 1 678.35 3182.7
## - sulphates 1 694.60 3220.5
## - volatile.acidity 1 709.85 3255.3
## - alcohol 1 792.02 3430.4
#model_stepwise
findCorrelation(
cor(df),
cutoff = 0.5,
verbose = TRUE,
names = TRUE
)
## Compare row 3 and column 1 with corr 0.672
## Means: 0.293 vs 0.19 so flagging column 3
## Compare row 1 and column 8 with corr 0.668
## Means: 0.245 vs 0.172 so flagging column 1
## Compare row 7 and column 6 with corr 0.668
## Means: 0.174 vs 0.169 so flagging column 7
## All correlations <= 0.5
## [1] "citric.acid" "fixed.acidity" "total.sulfur.dioxide"
ggcorrplot(correlation_df, hc.order = TRUE, type = "lower")
df_less_acid <- df %>%
select(-citric.acid, -fixed.acidity)
lm_less_acid <- lm(data = df_less_acid, quality ~ .)
summary(lm_less_acid)
##
## Call:
## lm(formula = quality ~ ., data = df_less_acid)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.66740 -0.37223 -0.04556 0.46264 2.03092
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 12.0575013 12.0089257 1.004 0.3155
## volatile.acidity -1.0127925 0.1009279 -10.035 < 2e-16 ***
## residual.sugar 0.0115046 0.0134606 0.855 0.3929
## chlorides -2.0490938 0.3992190 -5.133 3.21e-07 ***
## free.sulfur.dioxide 0.0048741 0.0021385 2.279 0.0228 *
## total.sulfur.dioxide -0.0035687 0.0006939 -5.143 3.03e-07 ***
## density -7.5668358 11.8648390 -0.638 0.5237
## pH -0.4919908 0.1210931 -4.063 5.08e-05 ***
## sulphates 0.9024434 0.1129657 7.989 2.60e-15 ***
## alcohol 0.2810022 0.0201992 13.912 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.648 on 1589 degrees of freedom
## Multiple R-squared: 0.3598, Adjusted R-squared: 0.3562
## F-statistic: 99.22 on 9 and 1589 DF, p-value: < 2.2e-16
plot(df)
colnames(df)
## [1] "fixed.acidity" "volatile.acidity" "citric.acid"
## [4] "residual.sugar" "chlorides" "free.sulfur.dioxide"
## [7] "total.sulfur.dioxide" "density" "pH"
## [10] "sulphates" "alcohol" "quality"
cols = c('fixed.acidity', 'volatile.acidity', 'citric.acid', 'residual.sugar', 'chlorides', 'free.sulfur.dioxide', 'total.sulfur.dioxide', 'density', 'pH', 'sulphates', 'alcohol')
pre_proc_val <- preProcess(train[,cols], method = c("center", "scale"))
train[,cols] = predict(pre_proc_val, train[,cols])
test[,cols] = predict(pre_proc_val, test[,cols])
summary(train)
## fixed.acidity volatile.acidity citric.acid residual.sugar
## Min. :-1.8982 Min. :-2.26862 Min. :-1.40589 Min. :-1.16322
## 1st Qu.:-0.7070 1st Qu.:-0.77506 1st Qu.:-0.88988 1st Qu.:-0.45567
## Median :-0.2532 Median :-0.05593 Median :-0.06428 Median :-0.24341
## Mean : 0.0000 Mean : 0.00000 Mean : 0.00000 Mean : 0.00000
## 3rd Qu.: 0.5410 3rd Qu.: 0.60787 3rd Qu.: 0.76132 3rd Qu.: 0.03961
## Max. : 4.2850 Max. : 5.80767 Max. : 3.75413 Max. : 9.16702
## chlorides free.sulfur.dioxide total.sulfur.dioxide density
## Min. :-1.52980 Min. :-1.4505 Min. :-1.2541 Min. :-3.52133
## 1st Qu.:-0.36645 1st Qu.:-0.8664 1st Qu.:-0.7603 1st Qu.:-0.60428
## Median :-0.16587 Median :-0.1849 Median :-0.2665 Median : 0.01593
## Mean : 0.00000 Mean : 0.0000 Mean : 0.0000 Mean : 0.00000
## 3rd Qu.: 0.05476 3rd Qu.: 0.4966 3rd Qu.: 0.4742 3rd Qu.: 0.59408
## Max. :10.48479 Max. : 5.0723 Max. : 7.4799 Max. : 3.63728
## pH sulphates alcohol quality
## Min. :-3.65381 Min. :-1.8950 Min. :-1.9054 Min. :3.00
## 1st Qu.:-0.63558 1st Qu.:-0.6400 1st Qu.:-0.8654 1st Qu.:5.00
## Median :-0.05762 Median :-0.2406 Median :-0.2036 Median :6.00
## Mean : 0.00000 Mean : 0.0000 Mean : 0.0000 Mean :5.63
## 3rd Qu.: 0.58456 3rd Qu.: 0.3869 3rd Qu.: 0.6473 3rd Qu.:6.00
## Max. : 4.50184 Max. : 7.6320 Max. : 4.2400 Max. :8.00
#generic LM
lm_2 <- lm(quality ~ ., data = train)
summary(lm_2)
##
## Call:
## lm(formula = quality ~ ., data = train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.67679 -0.36806 -0.05664 0.44772 1.98812
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.630027 0.019547 288.030 < 2e-16 ***
## fixed.acidity 0.005020 0.053098 0.095 0.925
## volatile.acidity -0.182301 0.025788 -7.069 2.76e-12 ***
## citric.acid 0.006733 0.033395 0.202 0.840
## residual.sugar 0.022515 0.024818 0.907 0.365
## chlorides -0.103942 0.023933 -4.343 1.53e-05 ***
## free.sulfur.dioxide 0.037472 0.027207 1.377 0.169
## total.sulfur.dioxide -0.117017 0.028773 -4.067 5.10e-05 ***
## density -0.016108 0.048469 -0.332 0.740
## pH -0.038438 0.035558 -1.081 0.280
## sulphates 0.161686 0.023577 6.858 1.16e-11 ***
## alcohol 0.273154 0.033538 8.145 1.02e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6539 on 1107 degrees of freedom
## Multiple R-squared: 0.3452, Adjusted R-squared: 0.3387
## F-statistic: 53.06 on 11 and 1107 DF, p-value: < 2.2e-16
cols_reg = c('fixed.acidity', 'volatile.acidity', 'citric.acid', 'residual.sugar', 'chlorides', 'free.sulfur.dioxide', 'total.sulfur.dioxide', 'density', 'pH', 'sulphates', 'alcohol', 'quality')
dummies <- dummyVars(quality ~ ., data = df[,cols_reg])
train_dummies = predict(dummies, newdata = train[,cols_reg])
test_dummies = predict(dummies, newdata = test[,cols_reg])
print(dim(train_dummies)); print(dim(test_dummies))
## [1] 1119 11
## [1] 480 11
x = as.matrix(train_dummies)
y_train = train$quality
x_test = as.matrix(test_dummies)
y_test = test$quality
lambdas <- 10^seq(2, -3, by = -.1)
ridge_reg = glmnet(x, y_train, nlambda = 25, alpha = 0, family = 'gaussian', lambda = lambdas)
summary(ridge_reg)
## Length Class Mode
## a0 51 -none- numeric
## beta 561 dgCMatrix S4
## df 51 -none- numeric
## dim 2 -none- numeric
## lambda 51 -none- numeric
## dev.ratio 51 -none- numeric
## nulldev 1 -none- numeric
## npasses 1 -none- numeric
## jerr 1 -none- numeric
## offset 1 -none- logical
## call 7 -none- call
## nobs 1 -none- numeric
cv_ridge <- cv.glmnet(x, y_train, alpha = 0, lambda = lambdas)
optimal_lambda <- cv_ridge$lambda.min
optimal_lambda
## [1] 0.05011872
# Compute R^2 from true and predicted values
eval_results <- function(true, predicted, df) {
SSE <- sum((predicted - true)^2)
SST <- sum((true - mean(true))^2)
R_square <- 1 - SSE / SST
RMSE = sqrt(SSE/nrow(df))
# Model performance metrics
data.frame(
RMSE = RMSE,
Rsquare = R_square
)
}
# Prediction and evaluation on train data
predictions_train <- predict(ridge_reg, s = optimal_lambda, newx = x)
eval_results(y_train, predictions_train, train)
## RMSE Rsquare
## 1 0.6508117 0.3443019
# Prediction and evaluation on test data
predictions_test <- predict(ridge_reg, s = optimal_lambda, newx = x_test)
eval_results(y_test, predictions_test, test)
## RMSE Rsquare
## 1 0.6415514 0.3810703
lambdas <- 10^seq(2, -3, by = -.1)
# Setting alpha = 1 implements lasso regression
lasso_reg <- cv.glmnet(x, y_train, alpha = 1, lambda = lambdas, standardize = TRUE, nfolds = 5)
# Best
lambda_best <- lasso_reg$lambda.min
lambda_best
## [1] 0.01584893
lasso_model <- glmnet(x, y_train, alpha = 1, lambda = lambda_best, standardize = TRUE)
predictions_train <- predict(lasso_model, s = lambda_best, newx = x)
eval_results(y_train, predictions_train, train)
## RMSE Rsquare
## 1 0.652377 0.3411439
predictions_test <- predict(lasso_model, s = lambda_best, newx = x_test)
eval_results(y_test, predictions_test, test)
## RMSE Rsquare
## 1 0.6450133 0.3743728
# Set training control
train_cont <- trainControl(method = "repeatedcv",
number = 10,
repeats = 5,
search = "random",
verboseIter = TRUE)
# Train the model
elastic_reg <- train(quality ~ .,
data = train,
method = "glmnet",
preProcess = c("center", "scale"),
tuneLength = 10,
trControl = train_cont)
## + Fold01.Rep1: alpha=0.64457, lambda=0.002748
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## + Fold03.Rep2: alpha=0.34217, lambda=3.683040
## - Fold03.Rep2: alpha=0.34217, lambda=3.683040
## + Fold03.Rep2: alpha=0.76305, lambda=0.037659
## - Fold03.Rep2: alpha=0.76305, lambda=0.037659
## + Fold03.Rep2: alpha=0.32620, lambda=0.010929
## - Fold03.Rep2: alpha=0.32620, lambda=0.010929
## + Fold03.Rep2: alpha=0.44663, lambda=0.001037
## - Fold03.Rep2: alpha=0.44663, lambda=0.001037
## + Fold03.Rep2: alpha=0.08757, lambda=0.012689
## - Fold03.Rep2: alpha=0.08757, lambda=0.012689
## + Fold03.Rep2: alpha=0.60040, lambda=0.003594
## - Fold03.Rep2: alpha=0.60040, lambda=0.003594
## + Fold03.Rep2: alpha=0.27368, lambda=0.453264
## - Fold03.Rep2: alpha=0.27368, lambda=0.453264
## + Fold03.Rep2: alpha=0.36848, lambda=4.961816
## - Fold03.Rep2: alpha=0.36848, lambda=4.961816
## + Fold04.Rep2: alpha=0.64457, lambda=0.002748
## - Fold04.Rep2: alpha=0.64457, lambda=0.002748
## + Fold04.Rep2: alpha=0.56029, lambda=0.304452
## - Fold04.Rep2: alpha=0.56029, lambda=0.304452
## + Fold04.Rep2: alpha=0.34217, lambda=3.683040
## - Fold04.Rep2: alpha=0.34217, lambda=3.683040
## + Fold04.Rep2: alpha=0.76305, lambda=0.037659
## - Fold04.Rep2: alpha=0.76305, lambda=0.037659
## + Fold04.Rep2: alpha=0.32620, lambda=0.010929
## - Fold04.Rep2: alpha=0.32620, lambda=0.010929
## + Fold04.Rep2: alpha=0.44663, lambda=0.001037
## - Fold04.Rep2: alpha=0.44663, lambda=0.001037
## + Fold04.Rep2: alpha=0.08757, lambda=0.012689
## - Fold04.Rep2: alpha=0.08757, lambda=0.012689
## + Fold04.Rep2: alpha=0.60040, lambda=0.003594
## - Fold04.Rep2: alpha=0.60040, lambda=0.003594
## + Fold04.Rep2: alpha=0.27368, lambda=0.453264
## - Fold04.Rep2: alpha=0.27368, lambda=0.453264
## + Fold04.Rep2: alpha=0.36848, lambda=4.961816
## - Fold04.Rep2: alpha=0.36848, lambda=4.961816
## + Fold05.Rep2: alpha=0.64457, lambda=0.002748
## - Fold05.Rep2: alpha=0.64457, lambda=0.002748
## + Fold05.Rep2: alpha=0.56029, lambda=0.304452
## - Fold05.Rep2: alpha=0.56029, lambda=0.304452
## + Fold05.Rep2: alpha=0.34217, lambda=3.683040
## - Fold05.Rep2: alpha=0.34217, lambda=3.683040
## + Fold05.Rep2: alpha=0.76305, lambda=0.037659
## - Fold05.Rep2: alpha=0.76305, lambda=0.037659
## + Fold05.Rep2: alpha=0.32620, lambda=0.010929
## - Fold05.Rep2: alpha=0.32620, lambda=0.010929
## + Fold05.Rep2: alpha=0.44663, lambda=0.001037
## - Fold05.Rep2: alpha=0.44663, lambda=0.001037
## + Fold05.Rep2: alpha=0.08757, lambda=0.012689
## - Fold05.Rep2: alpha=0.08757, lambda=0.012689
## + Fold05.Rep2: alpha=0.60040, lambda=0.003594
## - Fold05.Rep2: alpha=0.60040, lambda=0.003594
## + Fold05.Rep2: alpha=0.27368, lambda=0.453264
## - Fold05.Rep2: alpha=0.27368, lambda=0.453264
## + Fold05.Rep2: alpha=0.36848, lambda=4.961816
## - Fold05.Rep2: alpha=0.36848, lambda=4.961816
## + Fold06.Rep2: alpha=0.64457, lambda=0.002748
## - Fold06.Rep2: alpha=0.64457, lambda=0.002748
## + Fold06.Rep2: alpha=0.56029, lambda=0.304452
## - Fold06.Rep2: alpha=0.56029, lambda=0.304452
## + Fold06.Rep2: alpha=0.34217, lambda=3.683040
## - Fold06.Rep2: alpha=0.34217, lambda=3.683040
## + Fold06.Rep2: alpha=0.76305, lambda=0.037659
## - Fold06.Rep2: alpha=0.76305, lambda=0.037659
## + Fold06.Rep2: alpha=0.32620, lambda=0.010929
## - Fold06.Rep2: alpha=0.32620, lambda=0.010929
## + Fold06.Rep2: alpha=0.44663, lambda=0.001037
## - Fold06.Rep2: alpha=0.44663, lambda=0.001037
## + Fold06.Rep2: alpha=0.08757, lambda=0.012689
## - Fold06.Rep2: alpha=0.08757, lambda=0.012689
## + Fold06.Rep2: alpha=0.60040, lambda=0.003594
## - Fold06.Rep2: alpha=0.60040, lambda=0.003594
## + Fold06.Rep2: alpha=0.27368, lambda=0.453264
## - Fold06.Rep2: alpha=0.27368, lambda=0.453264
## + Fold06.Rep2: alpha=0.36848, lambda=4.961816
## - Fold06.Rep2: alpha=0.36848, lambda=4.961816
## + Fold07.Rep2: alpha=0.64457, lambda=0.002748
## - Fold07.Rep2: alpha=0.64457, lambda=0.002748
## + Fold07.Rep2: alpha=0.56029, lambda=0.304452
## - Fold07.Rep2: alpha=0.56029, lambda=0.304452
## + Fold07.Rep2: alpha=0.34217, lambda=3.683040
## - Fold07.Rep2: alpha=0.34217, lambda=3.683040
## + Fold07.Rep2: alpha=0.76305, lambda=0.037659
## - Fold07.Rep2: alpha=0.76305, lambda=0.037659
## + Fold07.Rep2: alpha=0.32620, lambda=0.010929
## - Fold07.Rep2: alpha=0.32620, lambda=0.010929
## + Fold07.Rep2: alpha=0.44663, lambda=0.001037
## - Fold07.Rep2: alpha=0.44663, lambda=0.001037
## + Fold07.Rep2: alpha=0.08757, lambda=0.012689
## - Fold07.Rep2: alpha=0.08757, lambda=0.012689
## + Fold07.Rep2: alpha=0.60040, lambda=0.003594
## - Fold07.Rep2: alpha=0.60040, lambda=0.003594
## + Fold07.Rep2: alpha=0.27368, lambda=0.453264
## - Fold07.Rep2: alpha=0.27368, lambda=0.453264
## + Fold07.Rep2: alpha=0.36848, lambda=4.961816
## - Fold07.Rep2: alpha=0.36848, lambda=4.961816
## + Fold08.Rep2: alpha=0.64457, lambda=0.002748
## - Fold08.Rep2: alpha=0.64457, lambda=0.002748
## + Fold08.Rep2: alpha=0.56029, lambda=0.304452
## - Fold08.Rep2: alpha=0.56029, lambda=0.304452
## + Fold08.Rep2: alpha=0.34217, lambda=3.683040
## - Fold08.Rep2: alpha=0.34217, lambda=3.683040
## + Fold08.Rep2: alpha=0.76305, lambda=0.037659
## - Fold08.Rep2: alpha=0.76305, lambda=0.037659
## + Fold08.Rep2: alpha=0.32620, lambda=0.010929
## - Fold08.Rep2: alpha=0.32620, lambda=0.010929
## + Fold08.Rep2: alpha=0.44663, lambda=0.001037
## - Fold08.Rep2: alpha=0.44663, lambda=0.001037
## + Fold08.Rep2: alpha=0.08757, lambda=0.012689
## - Fold08.Rep2: alpha=0.08757, lambda=0.012689
## + Fold08.Rep2: alpha=0.60040, lambda=0.003594
## - Fold08.Rep2: alpha=0.60040, lambda=0.003594
## + Fold08.Rep2: alpha=0.27368, lambda=0.453264
## - Fold08.Rep2: alpha=0.27368, lambda=0.453264
## + Fold08.Rep2: alpha=0.36848, lambda=4.961816
## - Fold08.Rep2: alpha=0.36848, lambda=4.961816
## + Fold09.Rep2: alpha=0.64457, lambda=0.002748
## - Fold09.Rep2: alpha=0.64457, lambda=0.002748
## + Fold09.Rep2: alpha=0.56029, lambda=0.304452
## - Fold09.Rep2: alpha=0.56029, lambda=0.304452
## + Fold09.Rep2: alpha=0.34217, lambda=3.683040
## - Fold09.Rep2: alpha=0.34217, lambda=3.683040
## + Fold09.Rep2: alpha=0.76305, lambda=0.037659
## - Fold09.Rep2: alpha=0.76305, lambda=0.037659
## + Fold09.Rep2: alpha=0.32620, lambda=0.010929
## - Fold09.Rep2: alpha=0.32620, lambda=0.010929
## + Fold09.Rep2: alpha=0.44663, lambda=0.001037
## - Fold09.Rep2: alpha=0.44663, lambda=0.001037
## + Fold09.Rep2: alpha=0.08757, lambda=0.012689
## - Fold09.Rep2: alpha=0.08757, lambda=0.012689
## + Fold09.Rep2: alpha=0.60040, lambda=0.003594
## - Fold09.Rep2: alpha=0.60040, lambda=0.003594
## + Fold09.Rep2: alpha=0.27368, lambda=0.453264
## - Fold09.Rep2: alpha=0.27368, lambda=0.453264
## + Fold09.Rep2: alpha=0.36848, lambda=4.961816
## - Fold09.Rep2: alpha=0.36848, lambda=4.961816
## + Fold10.Rep2: alpha=0.64457, lambda=0.002748
## - Fold10.Rep2: alpha=0.64457, lambda=0.002748
## + Fold10.Rep2: alpha=0.56029, lambda=0.304452
## - Fold10.Rep2: alpha=0.56029, lambda=0.304452
## + Fold10.Rep2: alpha=0.34217, lambda=3.683040
## - Fold10.Rep2: alpha=0.34217, lambda=3.683040
## + Fold10.Rep2: alpha=0.76305, lambda=0.037659
## - Fold10.Rep2: alpha=0.76305, lambda=0.037659
## + Fold10.Rep2: alpha=0.32620, lambda=0.010929
## - Fold10.Rep2: alpha=0.32620, lambda=0.010929
## + Fold10.Rep2: alpha=0.44663, lambda=0.001037
## - Fold10.Rep2: alpha=0.44663, lambda=0.001037
## + Fold10.Rep2: alpha=0.08757, lambda=0.012689
## - Fold10.Rep2: alpha=0.08757, lambda=0.012689
## + Fold10.Rep2: alpha=0.60040, lambda=0.003594
## - Fold10.Rep2: alpha=0.60040, lambda=0.003594
## + Fold10.Rep2: alpha=0.27368, lambda=0.453264
## - Fold10.Rep2: alpha=0.27368, lambda=0.453264
## + Fold10.Rep2: alpha=0.36848, lambda=4.961816
## - Fold10.Rep2: alpha=0.36848, lambda=4.961816
## + Fold01.Rep3: alpha=0.64457, lambda=0.002748
## - Fold01.Rep3: alpha=0.64457, lambda=0.002748
## + Fold01.Rep3: alpha=0.56029, lambda=0.304452
## - Fold01.Rep3: alpha=0.56029, lambda=0.304452
## + Fold01.Rep3: alpha=0.34217, lambda=3.683040
## - Fold01.Rep3: alpha=0.34217, lambda=3.683040
## + Fold01.Rep3: alpha=0.76305, lambda=0.037659
## - Fold01.Rep3: alpha=0.76305, lambda=0.037659
## + Fold01.Rep3: alpha=0.32620, lambda=0.010929
## - Fold01.Rep3: alpha=0.32620, lambda=0.010929
## + Fold01.Rep3: alpha=0.44663, lambda=0.001037
## - Fold01.Rep3: alpha=0.44663, lambda=0.001037
## + Fold01.Rep3: alpha=0.08757, lambda=0.012689
## - Fold01.Rep3: alpha=0.08757, lambda=0.012689
## + Fold01.Rep3: alpha=0.60040, lambda=0.003594
## - Fold01.Rep3: alpha=0.60040, lambda=0.003594
## + Fold01.Rep3: alpha=0.27368, lambda=0.453264
## - Fold01.Rep3: alpha=0.27368, lambda=0.453264
## + Fold01.Rep3: alpha=0.36848, lambda=4.961816
## - Fold01.Rep3: alpha=0.36848, lambda=4.961816
## + Fold02.Rep3: alpha=0.64457, lambda=0.002748
## - Fold02.Rep3: alpha=0.64457, lambda=0.002748
## + Fold02.Rep3: alpha=0.56029, lambda=0.304452
## - Fold02.Rep3: alpha=0.56029, lambda=0.304452
## + Fold02.Rep3: alpha=0.34217, lambda=3.683040
## - Fold02.Rep3: alpha=0.34217, lambda=3.683040
## + Fold02.Rep3: alpha=0.76305, lambda=0.037659
## - Fold02.Rep3: alpha=0.76305, lambda=0.037659
## + Fold02.Rep3: alpha=0.32620, lambda=0.010929
## - Fold02.Rep3: alpha=0.32620, lambda=0.010929
## + Fold02.Rep3: alpha=0.44663, lambda=0.001037
## - Fold02.Rep3: alpha=0.44663, lambda=0.001037
## + Fold02.Rep3: alpha=0.08757, lambda=0.012689
## - Fold02.Rep3: alpha=0.08757, lambda=0.012689
## + Fold02.Rep3: alpha=0.60040, lambda=0.003594
## - Fold02.Rep3: alpha=0.60040, lambda=0.003594
## + Fold02.Rep3: alpha=0.27368, lambda=0.453264
## - Fold02.Rep3: alpha=0.27368, lambda=0.453264
## + Fold02.Rep3: alpha=0.36848, lambda=4.961816
## - Fold02.Rep3: alpha=0.36848, lambda=4.961816
## + Fold03.Rep3: alpha=0.64457, lambda=0.002748
## - Fold03.Rep3: alpha=0.64457, lambda=0.002748
## + Fold03.Rep3: alpha=0.56029, lambda=0.304452
## - Fold03.Rep3: alpha=0.56029, lambda=0.304452
## + Fold03.Rep3: alpha=0.34217, lambda=3.683040
## - Fold03.Rep3: alpha=0.34217, lambda=3.683040
## + Fold03.Rep3: alpha=0.76305, lambda=0.037659
## - Fold03.Rep3: alpha=0.76305, lambda=0.037659
## + Fold03.Rep3: alpha=0.32620, lambda=0.010929
## - Fold03.Rep3: alpha=0.32620, lambda=0.010929
## + Fold03.Rep3: alpha=0.44663, lambda=0.001037
## - Fold03.Rep3: alpha=0.44663, lambda=0.001037
## + Fold03.Rep3: alpha=0.08757, lambda=0.012689
## - Fold03.Rep3: alpha=0.08757, lambda=0.012689
## + Fold03.Rep3: alpha=0.60040, lambda=0.003594
## - Fold03.Rep3: alpha=0.60040, lambda=0.003594
## + Fold03.Rep3: alpha=0.27368, lambda=0.453264
## - Fold03.Rep3: alpha=0.27368, lambda=0.453264
## + Fold03.Rep3: alpha=0.36848, lambda=4.961816
## - Fold03.Rep3: alpha=0.36848, lambda=4.961816
## + Fold04.Rep3: alpha=0.64457, lambda=0.002748
## - Fold04.Rep3: alpha=0.64457, lambda=0.002748
## + Fold04.Rep3: alpha=0.56029, lambda=0.304452
## - Fold04.Rep3: alpha=0.56029, lambda=0.304452
## + Fold04.Rep3: alpha=0.34217, lambda=3.683040
## - Fold04.Rep3: alpha=0.34217, lambda=3.683040
## + Fold04.Rep3: alpha=0.76305, lambda=0.037659
## - Fold04.Rep3: alpha=0.76305, lambda=0.037659
## + Fold04.Rep3: alpha=0.32620, lambda=0.010929
## - Fold04.Rep3: alpha=0.32620, lambda=0.010929
## + Fold04.Rep3: alpha=0.44663, lambda=0.001037
## - Fold04.Rep3: alpha=0.44663, lambda=0.001037
## + Fold04.Rep3: alpha=0.08757, lambda=0.012689
## - Fold04.Rep3: alpha=0.08757, lambda=0.012689
## + Fold04.Rep3: alpha=0.60040, lambda=0.003594
## - Fold04.Rep3: alpha=0.60040, lambda=0.003594
## + Fold04.Rep3: alpha=0.27368, lambda=0.453264
## - Fold04.Rep3: alpha=0.27368, lambda=0.453264
## + Fold04.Rep3: alpha=0.36848, lambda=4.961816
## - Fold04.Rep3: alpha=0.36848, lambda=4.961816
## + Fold05.Rep3: alpha=0.64457, lambda=0.002748
## - Fold05.Rep3: alpha=0.64457, lambda=0.002748
## + Fold05.Rep3: alpha=0.56029, lambda=0.304452
## - Fold05.Rep3: alpha=0.56029, lambda=0.304452
## + Fold05.Rep3: alpha=0.34217, lambda=3.683040
## - Fold05.Rep3: alpha=0.34217, lambda=3.683040
## + Fold05.Rep3: alpha=0.76305, lambda=0.037659
## - Fold05.Rep3: alpha=0.76305, lambda=0.037659
## + Fold05.Rep3: alpha=0.32620, lambda=0.010929
## - Fold05.Rep3: alpha=0.32620, lambda=0.010929
## + Fold05.Rep3: alpha=0.44663, lambda=0.001037
## - Fold05.Rep3: alpha=0.44663, lambda=0.001037
## + Fold05.Rep3: alpha=0.08757, lambda=0.012689
## - Fold05.Rep3: alpha=0.08757, lambda=0.012689
## + Fold05.Rep3: alpha=0.60040, lambda=0.003594
## - Fold05.Rep3: alpha=0.60040, lambda=0.003594
## + Fold05.Rep3: alpha=0.27368, lambda=0.453264
## - Fold05.Rep3: alpha=0.27368, lambda=0.453264
## + Fold05.Rep3: alpha=0.36848, lambda=4.961816
## - Fold05.Rep3: alpha=0.36848, lambda=4.961816
## + Fold06.Rep3: alpha=0.64457, lambda=0.002748
## - Fold06.Rep3: alpha=0.64457, lambda=0.002748
## + Fold06.Rep3: alpha=0.56029, lambda=0.304452
## - Fold06.Rep3: alpha=0.56029, lambda=0.304452
## + Fold06.Rep3: alpha=0.34217, lambda=3.683040
## - Fold06.Rep3: alpha=0.34217, lambda=3.683040
## + Fold06.Rep3: alpha=0.76305, lambda=0.037659
## - Fold06.Rep3: alpha=0.76305, lambda=0.037659
## + Fold06.Rep3: alpha=0.32620, lambda=0.010929
## - Fold06.Rep3: alpha=0.32620, lambda=0.010929
## + Fold06.Rep3: alpha=0.44663, lambda=0.001037
## - Fold06.Rep3: alpha=0.44663, lambda=0.001037
## + Fold06.Rep3: alpha=0.08757, lambda=0.012689
## - Fold06.Rep3: alpha=0.08757, lambda=0.012689
## + Fold06.Rep3: alpha=0.60040, lambda=0.003594
## - Fold06.Rep3: alpha=0.60040, lambda=0.003594
## + Fold06.Rep3: alpha=0.27368, lambda=0.453264
## - Fold06.Rep3: alpha=0.27368, lambda=0.453264
## + Fold06.Rep3: alpha=0.36848, lambda=4.961816
## - Fold06.Rep3: alpha=0.36848, lambda=4.961816
## + Fold07.Rep3: alpha=0.64457, lambda=0.002748
## - Fold07.Rep3: alpha=0.64457, lambda=0.002748
## + Fold07.Rep3: alpha=0.56029, lambda=0.304452
## - Fold07.Rep3: alpha=0.56029, lambda=0.304452
## + Fold07.Rep3: alpha=0.34217, lambda=3.683040
## - Fold07.Rep3: alpha=0.34217, lambda=3.683040
## + Fold07.Rep3: alpha=0.76305, lambda=0.037659
## - Fold07.Rep3: alpha=0.76305, lambda=0.037659
## + Fold07.Rep3: alpha=0.32620, lambda=0.010929
## - Fold07.Rep3: alpha=0.32620, lambda=0.010929
## + Fold07.Rep3: alpha=0.44663, lambda=0.001037
## - Fold07.Rep3: alpha=0.44663, lambda=0.001037
## + Fold07.Rep3: alpha=0.08757, lambda=0.012689
## - Fold07.Rep3: alpha=0.08757, lambda=0.012689
## + Fold07.Rep3: alpha=0.60040, lambda=0.003594
## - Fold07.Rep3: alpha=0.60040, lambda=0.003594
## + Fold07.Rep3: alpha=0.27368, lambda=0.453264
## - Fold07.Rep3: alpha=0.27368, lambda=0.453264
## + Fold07.Rep3: alpha=0.36848, lambda=4.961816
## - Fold07.Rep3: alpha=0.36848, lambda=4.961816
## + Fold08.Rep3: alpha=0.64457, lambda=0.002748
## - Fold08.Rep3: alpha=0.64457, lambda=0.002748
## + Fold08.Rep3: alpha=0.56029, lambda=0.304452
## - Fold08.Rep3: alpha=0.56029, lambda=0.304452
## + Fold08.Rep3: alpha=0.34217, lambda=3.683040
## - Fold08.Rep3: alpha=0.34217, lambda=3.683040
## + Fold08.Rep3: alpha=0.76305, lambda=0.037659
## - Fold08.Rep3: alpha=0.76305, lambda=0.037659
## + Fold08.Rep3: alpha=0.32620, lambda=0.010929
## - Fold08.Rep3: alpha=0.32620, lambda=0.010929
## + Fold08.Rep3: alpha=0.44663, lambda=0.001037
## - Fold08.Rep3: alpha=0.44663, lambda=0.001037
## + Fold08.Rep3: alpha=0.08757, lambda=0.012689
## - Fold08.Rep3: alpha=0.08757, lambda=0.012689
## + Fold08.Rep3: alpha=0.60040, lambda=0.003594
## - Fold08.Rep3: alpha=0.60040, lambda=0.003594
## + Fold08.Rep3: alpha=0.27368, lambda=0.453264
## - Fold08.Rep3: alpha=0.27368, lambda=0.453264
## + Fold08.Rep3: alpha=0.36848, lambda=4.961816
## - Fold08.Rep3: alpha=0.36848, lambda=4.961816
## + Fold09.Rep3: alpha=0.64457, lambda=0.002748
## - Fold09.Rep3: alpha=0.64457, lambda=0.002748
## + Fold09.Rep3: alpha=0.56029, lambda=0.304452
## - Fold09.Rep3: alpha=0.56029, lambda=0.304452
## + Fold09.Rep3: alpha=0.34217, lambda=3.683040
## - Fold09.Rep3: alpha=0.34217, lambda=3.683040
## + Fold09.Rep3: alpha=0.76305, lambda=0.037659
## - Fold09.Rep3: alpha=0.76305, lambda=0.037659
## + Fold09.Rep3: alpha=0.32620, lambda=0.010929
## - Fold09.Rep3: alpha=0.32620, lambda=0.010929
## + Fold09.Rep3: alpha=0.44663, lambda=0.001037
## - Fold09.Rep3: alpha=0.44663, lambda=0.001037
## + Fold09.Rep3: alpha=0.08757, lambda=0.012689
## - Fold09.Rep3: alpha=0.08757, lambda=0.012689
## + Fold09.Rep3: alpha=0.60040, lambda=0.003594
## - Fold09.Rep3: alpha=0.60040, lambda=0.003594
## + Fold09.Rep3: alpha=0.27368, lambda=0.453264
## - Fold09.Rep3: alpha=0.27368, lambda=0.453264
## + Fold09.Rep3: alpha=0.36848, lambda=4.961816
## - Fold09.Rep3: alpha=0.36848, lambda=4.961816
## + Fold10.Rep3: alpha=0.64457, lambda=0.002748
## - Fold10.Rep3: alpha=0.64457, lambda=0.002748
## + Fold10.Rep3: alpha=0.56029, lambda=0.304452
## - Fold10.Rep3: alpha=0.56029, lambda=0.304452
## + Fold10.Rep3: alpha=0.34217, lambda=3.683040
## - Fold10.Rep3: alpha=0.34217, lambda=3.683040
## + Fold10.Rep3: alpha=0.76305, lambda=0.037659
## - Fold10.Rep3: alpha=0.76305, lambda=0.037659
## + Fold10.Rep3: alpha=0.32620, lambda=0.010929
## - Fold10.Rep3: alpha=0.32620, lambda=0.010929
## + Fold10.Rep3: alpha=0.44663, lambda=0.001037
## - Fold10.Rep3: alpha=0.44663, lambda=0.001037
## + Fold10.Rep3: alpha=0.08757, lambda=0.012689
## - Fold10.Rep3: alpha=0.08757, lambda=0.012689
## + Fold10.Rep3: alpha=0.60040, lambda=0.003594
## - Fold10.Rep3: alpha=0.60040, lambda=0.003594
## + Fold10.Rep3: alpha=0.27368, lambda=0.453264
## - Fold10.Rep3: alpha=0.27368, lambda=0.453264
## + Fold10.Rep3: alpha=0.36848, lambda=4.961816
## - Fold10.Rep3: alpha=0.36848, lambda=4.961816
## + Fold01.Rep4: alpha=0.64457, lambda=0.002748
## - Fold01.Rep4: alpha=0.64457, lambda=0.002748
## + Fold01.Rep4: alpha=0.56029, lambda=0.304452
## - Fold01.Rep4: alpha=0.56029, lambda=0.304452
## + Fold01.Rep4: alpha=0.34217, lambda=3.683040
## - Fold01.Rep4: alpha=0.34217, lambda=3.683040
## + Fold01.Rep4: alpha=0.76305, lambda=0.037659
## - Fold01.Rep4: alpha=0.76305, lambda=0.037659
## + Fold01.Rep4: alpha=0.32620, lambda=0.010929
## - Fold01.Rep4: alpha=0.32620, lambda=0.010929
## + Fold01.Rep4: alpha=0.44663, lambda=0.001037
## - Fold01.Rep4: alpha=0.44663, lambda=0.001037
## + Fold01.Rep4: alpha=0.08757, lambda=0.012689
## - Fold01.Rep4: alpha=0.08757, lambda=0.012689
## + Fold01.Rep4: alpha=0.60040, lambda=0.003594
## - Fold01.Rep4: alpha=0.60040, lambda=0.003594
## + Fold01.Rep4: alpha=0.27368, lambda=0.453264
## - Fold01.Rep4: alpha=0.27368, lambda=0.453264
## + Fold01.Rep4: alpha=0.36848, lambda=4.961816
## - Fold01.Rep4: alpha=0.36848, lambda=4.961816
## + Fold02.Rep4: alpha=0.64457, lambda=0.002748
## - Fold02.Rep4: alpha=0.64457, lambda=0.002748
## + Fold02.Rep4: alpha=0.56029, lambda=0.304452
## - Fold02.Rep4: alpha=0.56029, lambda=0.304452
## + Fold02.Rep4: alpha=0.34217, lambda=3.683040
## - Fold02.Rep4: alpha=0.34217, lambda=3.683040
## + Fold02.Rep4: alpha=0.76305, lambda=0.037659
## - Fold02.Rep4: alpha=0.76305, lambda=0.037659
## + Fold02.Rep4: alpha=0.32620, lambda=0.010929
## - Fold02.Rep4: alpha=0.32620, lambda=0.010929
## + Fold02.Rep4: alpha=0.44663, lambda=0.001037
## - Fold02.Rep4: alpha=0.44663, lambda=0.001037
## + Fold02.Rep4: alpha=0.08757, lambda=0.012689
## - Fold02.Rep4: alpha=0.08757, lambda=0.012689
## + Fold02.Rep4: alpha=0.60040, lambda=0.003594
## - Fold02.Rep4: alpha=0.60040, lambda=0.003594
## + Fold02.Rep4: alpha=0.27368, lambda=0.453264
## - Fold02.Rep4: alpha=0.27368, lambda=0.453264
## + Fold02.Rep4: alpha=0.36848, lambda=4.961816
## - Fold02.Rep4: alpha=0.36848, lambda=4.961816
## + Fold03.Rep4: alpha=0.64457, lambda=0.002748
## - Fold03.Rep4: alpha=0.64457, lambda=0.002748
## + Fold03.Rep4: alpha=0.56029, lambda=0.304452
## - Fold03.Rep4: alpha=0.56029, lambda=0.304452
## + Fold03.Rep4: alpha=0.34217, lambda=3.683040
## - Fold03.Rep4: alpha=0.34217, lambda=3.683040
## + Fold03.Rep4: alpha=0.76305, lambda=0.037659
## - Fold03.Rep4: alpha=0.76305, lambda=0.037659
## + Fold03.Rep4: alpha=0.32620, lambda=0.010929
## - Fold03.Rep4: alpha=0.32620, lambda=0.010929
## + Fold03.Rep4: alpha=0.44663, lambda=0.001037
## - Fold03.Rep4: alpha=0.44663, lambda=0.001037
## + Fold03.Rep4: alpha=0.08757, lambda=0.012689
## - Fold03.Rep4: alpha=0.08757, lambda=0.012689
## + Fold03.Rep4: alpha=0.60040, lambda=0.003594
## - Fold03.Rep4: alpha=0.60040, lambda=0.003594
## + Fold03.Rep4: alpha=0.27368, lambda=0.453264
## - Fold03.Rep4: alpha=0.27368, lambda=0.453264
## + Fold03.Rep4: alpha=0.36848, lambda=4.961816
## - Fold03.Rep4: alpha=0.36848, lambda=4.961816
## + Fold04.Rep4: alpha=0.64457, lambda=0.002748
## - Fold04.Rep4: alpha=0.64457, lambda=0.002748
## + Fold04.Rep4: alpha=0.56029, lambda=0.304452
## - Fold04.Rep4: alpha=0.56029, lambda=0.304452
## + Fold04.Rep4: alpha=0.34217, lambda=3.683040
## - Fold04.Rep4: alpha=0.34217, lambda=3.683040
## + Fold04.Rep4: alpha=0.76305, lambda=0.037659
## - Fold04.Rep4: alpha=0.76305, lambda=0.037659
## + Fold04.Rep4: alpha=0.32620, lambda=0.010929
## - Fold04.Rep4: alpha=0.32620, lambda=0.010929
## + Fold04.Rep4: alpha=0.44663, lambda=0.001037
## - Fold04.Rep4: alpha=0.44663, lambda=0.001037
## + Fold04.Rep4: alpha=0.08757, lambda=0.012689
## - Fold04.Rep4: alpha=0.08757, lambda=0.012689
## + Fold04.Rep4: alpha=0.60040, lambda=0.003594
## - Fold04.Rep4: alpha=0.60040, lambda=0.003594
## + Fold04.Rep4: alpha=0.27368, lambda=0.453264
## - Fold04.Rep4: alpha=0.27368, lambda=0.453264
## + Fold04.Rep4: alpha=0.36848, lambda=4.961816
## - Fold04.Rep4: alpha=0.36848, lambda=4.961816
## + Fold05.Rep4: alpha=0.64457, lambda=0.002748
## - Fold05.Rep4: alpha=0.64457, lambda=0.002748
## + Fold05.Rep4: alpha=0.56029, lambda=0.304452
## - Fold05.Rep4: alpha=0.56029, lambda=0.304452
## + Fold05.Rep4: alpha=0.34217, lambda=3.683040
## - Fold05.Rep4: alpha=0.34217, lambda=3.683040
## + Fold05.Rep4: alpha=0.76305, lambda=0.037659
## - Fold05.Rep4: alpha=0.76305, lambda=0.037659
## + Fold05.Rep4: alpha=0.32620, lambda=0.010929
## - Fold05.Rep4: alpha=0.32620, lambda=0.010929
## + Fold05.Rep4: alpha=0.44663, lambda=0.001037
## - Fold05.Rep4: alpha=0.44663, lambda=0.001037
## + Fold05.Rep4: alpha=0.08757, lambda=0.012689
## - Fold05.Rep4: alpha=0.08757, lambda=0.012689
## + Fold05.Rep4: alpha=0.60040, lambda=0.003594
## - Fold05.Rep4: alpha=0.60040, lambda=0.003594
## + Fold05.Rep4: alpha=0.27368, lambda=0.453264
## - Fold05.Rep4: alpha=0.27368, lambda=0.453264
## + Fold05.Rep4: alpha=0.36848, lambda=4.961816
## - Fold05.Rep4: alpha=0.36848, lambda=4.961816
## + Fold06.Rep4: alpha=0.64457, lambda=0.002748
## - Fold06.Rep4: alpha=0.64457, lambda=0.002748
## + Fold06.Rep4: alpha=0.56029, lambda=0.304452
## - Fold06.Rep4: alpha=0.56029, lambda=0.304452
## + Fold06.Rep4: alpha=0.34217, lambda=3.683040
## - Fold06.Rep4: alpha=0.34217, lambda=3.683040
## + Fold06.Rep4: alpha=0.76305, lambda=0.037659
## - Fold06.Rep4: alpha=0.76305, lambda=0.037659
## + Fold06.Rep4: alpha=0.32620, lambda=0.010929
## - Fold06.Rep4: alpha=0.32620, lambda=0.010929
## + Fold06.Rep4: alpha=0.44663, lambda=0.001037
## - Fold06.Rep4: alpha=0.44663, lambda=0.001037
## + Fold06.Rep4: alpha=0.08757, lambda=0.012689
## - Fold06.Rep4: alpha=0.08757, lambda=0.012689
## + Fold06.Rep4: alpha=0.60040, lambda=0.003594
## - Fold06.Rep4: alpha=0.60040, lambda=0.003594
## + Fold06.Rep4: alpha=0.27368, lambda=0.453264
## - Fold06.Rep4: alpha=0.27368, lambda=0.453264
## + Fold06.Rep4: alpha=0.36848, lambda=4.961816
## - Fold06.Rep4: alpha=0.36848, lambda=4.961816
## + Fold07.Rep4: alpha=0.64457, lambda=0.002748
## - Fold07.Rep4: alpha=0.64457, lambda=0.002748
## + Fold07.Rep4: alpha=0.56029, lambda=0.304452
## - Fold07.Rep4: alpha=0.56029, lambda=0.304452
## + Fold07.Rep4: alpha=0.34217, lambda=3.683040
## - Fold07.Rep4: alpha=0.34217, lambda=3.683040
## + Fold07.Rep4: alpha=0.76305, lambda=0.037659
## - Fold07.Rep4: alpha=0.76305, lambda=0.037659
## + Fold07.Rep4: alpha=0.32620, lambda=0.010929
## - Fold07.Rep4: alpha=0.32620, lambda=0.010929
## + Fold07.Rep4: alpha=0.44663, lambda=0.001037
## - Fold07.Rep4: alpha=0.44663, lambda=0.001037
## + Fold07.Rep4: alpha=0.08757, lambda=0.012689
## - Fold07.Rep4: alpha=0.08757, lambda=0.012689
## + Fold07.Rep4: alpha=0.60040, lambda=0.003594
## - Fold07.Rep4: alpha=0.60040, lambda=0.003594
## + Fold07.Rep4: alpha=0.27368, lambda=0.453264
## - Fold07.Rep4: alpha=0.27368, lambda=0.453264
## + Fold07.Rep4: alpha=0.36848, lambda=4.961816
## - Fold07.Rep4: alpha=0.36848, lambda=4.961816
## + Fold08.Rep4: alpha=0.64457, lambda=0.002748
## - Fold08.Rep4: alpha=0.64457, lambda=0.002748
## + Fold08.Rep4: alpha=0.56029, lambda=0.304452
## - Fold08.Rep4: alpha=0.56029, lambda=0.304452
## + Fold08.Rep4: alpha=0.34217, lambda=3.683040
## - Fold08.Rep4: alpha=0.34217, lambda=3.683040
## + Fold08.Rep4: alpha=0.76305, lambda=0.037659
## - Fold08.Rep4: alpha=0.76305, lambda=0.037659
## + Fold08.Rep4: alpha=0.32620, lambda=0.010929
## - Fold08.Rep4: alpha=0.32620, lambda=0.010929
## + Fold08.Rep4: alpha=0.44663, lambda=0.001037
## - Fold08.Rep4: alpha=0.44663, lambda=0.001037
## + Fold08.Rep4: alpha=0.08757, lambda=0.012689
## - Fold08.Rep4: alpha=0.08757, lambda=0.012689
## + Fold08.Rep4: alpha=0.60040, lambda=0.003594
## - Fold08.Rep4: alpha=0.60040, lambda=0.003594
## + Fold08.Rep4: alpha=0.27368, lambda=0.453264
## - Fold08.Rep4: alpha=0.27368, lambda=0.453264
## + Fold08.Rep4: alpha=0.36848, lambda=4.961816
## - Fold08.Rep4: alpha=0.36848, lambda=4.961816
## + Fold09.Rep4: alpha=0.64457, lambda=0.002748
## - Fold09.Rep4: alpha=0.64457, lambda=0.002748
## + Fold09.Rep4: alpha=0.56029, lambda=0.304452
## - Fold09.Rep4: alpha=0.56029, lambda=0.304452
## + Fold09.Rep4: alpha=0.34217, lambda=3.683040
## - Fold09.Rep4: alpha=0.34217, lambda=3.683040
## + Fold09.Rep4: alpha=0.76305, lambda=0.037659
## - Fold09.Rep4: alpha=0.76305, lambda=0.037659
## + Fold09.Rep4: alpha=0.32620, lambda=0.010929
## - Fold09.Rep4: alpha=0.32620, lambda=0.010929
## + Fold09.Rep4: alpha=0.44663, lambda=0.001037
## - Fold09.Rep4: alpha=0.44663, lambda=0.001037
## + Fold09.Rep4: alpha=0.08757, lambda=0.012689
## - Fold09.Rep4: alpha=0.08757, lambda=0.012689
## + Fold09.Rep4: alpha=0.60040, lambda=0.003594
## - Fold09.Rep4: alpha=0.60040, lambda=0.003594
## + Fold09.Rep4: alpha=0.27368, lambda=0.453264
## - Fold09.Rep4: alpha=0.27368, lambda=0.453264
## + Fold09.Rep4: alpha=0.36848, lambda=4.961816
## - Fold09.Rep4: alpha=0.36848, lambda=4.961816
## + Fold10.Rep4: alpha=0.64457, lambda=0.002748
## - Fold10.Rep4: alpha=0.64457, lambda=0.002748
## + Fold10.Rep4: alpha=0.56029, lambda=0.304452
## - Fold10.Rep4: alpha=0.56029, lambda=0.304452
## + Fold10.Rep4: alpha=0.34217, lambda=3.683040
## - Fold10.Rep4: alpha=0.34217, lambda=3.683040
## + Fold10.Rep4: alpha=0.76305, lambda=0.037659
## - Fold10.Rep4: alpha=0.76305, lambda=0.037659
## + Fold10.Rep4: alpha=0.32620, lambda=0.010929
## - Fold10.Rep4: alpha=0.32620, lambda=0.010929
## + Fold10.Rep4: alpha=0.44663, lambda=0.001037
## - Fold10.Rep4: alpha=0.44663, lambda=0.001037
## + Fold10.Rep4: alpha=0.08757, lambda=0.012689
## - Fold10.Rep4: alpha=0.08757, lambda=0.012689
## + Fold10.Rep4: alpha=0.60040, lambda=0.003594
## - Fold10.Rep4: alpha=0.60040, lambda=0.003594
## + Fold10.Rep4: alpha=0.27368, lambda=0.453264
## - Fold10.Rep4: alpha=0.27368, lambda=0.453264
## + Fold10.Rep4: alpha=0.36848, lambda=4.961816
## - Fold10.Rep4: alpha=0.36848, lambda=4.961816
## + Fold01.Rep5: alpha=0.64457, lambda=0.002748
## - Fold01.Rep5: alpha=0.64457, lambda=0.002748
## + Fold01.Rep5: alpha=0.56029, lambda=0.304452
## - Fold01.Rep5: alpha=0.56029, lambda=0.304452
## + Fold01.Rep5: alpha=0.34217, lambda=3.683040
## - Fold01.Rep5: alpha=0.34217, lambda=3.683040
## + Fold01.Rep5: alpha=0.76305, lambda=0.037659
## - Fold01.Rep5: alpha=0.76305, lambda=0.037659
## + Fold01.Rep5: alpha=0.32620, lambda=0.010929
## - Fold01.Rep5: alpha=0.32620, lambda=0.010929
## + Fold01.Rep5: alpha=0.44663, lambda=0.001037
## - Fold01.Rep5: alpha=0.44663, lambda=0.001037
## + Fold01.Rep5: alpha=0.08757, lambda=0.012689
## - Fold01.Rep5: alpha=0.08757, lambda=0.012689
## + Fold01.Rep5: alpha=0.60040, lambda=0.003594
## - Fold01.Rep5: alpha=0.60040, lambda=0.003594
## + Fold01.Rep5: alpha=0.27368, lambda=0.453264
## - Fold01.Rep5: alpha=0.27368, lambda=0.453264
## + Fold01.Rep5: alpha=0.36848, lambda=4.961816
## - Fold01.Rep5: alpha=0.36848, lambda=4.961816
## + Fold02.Rep5: alpha=0.64457, lambda=0.002748
## - Fold02.Rep5: alpha=0.64457, lambda=0.002748
## + Fold02.Rep5: alpha=0.56029, lambda=0.304452
## - Fold02.Rep5: alpha=0.56029, lambda=0.304452
## + Fold02.Rep5: alpha=0.34217, lambda=3.683040
## - Fold02.Rep5: alpha=0.34217, lambda=3.683040
## + Fold02.Rep5: alpha=0.76305, lambda=0.037659
## - Fold02.Rep5: alpha=0.76305, lambda=0.037659
## + Fold02.Rep5: alpha=0.32620, lambda=0.010929
## - Fold02.Rep5: alpha=0.32620, lambda=0.010929
## + Fold02.Rep5: alpha=0.44663, lambda=0.001037
## - Fold02.Rep5: alpha=0.44663, lambda=0.001037
## + Fold02.Rep5: alpha=0.08757, lambda=0.012689
## - Fold02.Rep5: alpha=0.08757, lambda=0.012689
## + Fold02.Rep5: alpha=0.60040, lambda=0.003594
## - Fold02.Rep5: alpha=0.60040, lambda=0.003594
## + Fold02.Rep5: alpha=0.27368, lambda=0.453264
## - Fold02.Rep5: alpha=0.27368, lambda=0.453264
## + Fold02.Rep5: alpha=0.36848, lambda=4.961816
## - Fold02.Rep5: alpha=0.36848, lambda=4.961816
## + Fold03.Rep5: alpha=0.64457, lambda=0.002748
## - Fold03.Rep5: alpha=0.64457, lambda=0.002748
## + Fold03.Rep5: alpha=0.56029, lambda=0.304452
## - Fold03.Rep5: alpha=0.56029, lambda=0.304452
## + Fold03.Rep5: alpha=0.34217, lambda=3.683040
## - Fold03.Rep5: alpha=0.34217, lambda=3.683040
## + Fold03.Rep5: alpha=0.76305, lambda=0.037659
## - Fold03.Rep5: alpha=0.76305, lambda=0.037659
## + Fold03.Rep5: alpha=0.32620, lambda=0.010929
## - Fold03.Rep5: alpha=0.32620, lambda=0.010929
## + Fold03.Rep5: alpha=0.44663, lambda=0.001037
## - Fold03.Rep5: alpha=0.44663, lambda=0.001037
## + Fold03.Rep5: alpha=0.08757, lambda=0.012689
## - Fold03.Rep5: alpha=0.08757, lambda=0.012689
## + Fold03.Rep5: alpha=0.60040, lambda=0.003594
## - Fold03.Rep5: alpha=0.60040, lambda=0.003594
## + Fold03.Rep5: alpha=0.27368, lambda=0.453264
## - Fold03.Rep5: alpha=0.27368, lambda=0.453264
## + Fold03.Rep5: alpha=0.36848, lambda=4.961816
## - Fold03.Rep5: alpha=0.36848, lambda=4.961816
## + Fold04.Rep5: alpha=0.64457, lambda=0.002748
## - Fold04.Rep5: alpha=0.64457, lambda=0.002748
## + Fold04.Rep5: alpha=0.56029, lambda=0.304452
## - Fold04.Rep5: alpha=0.56029, lambda=0.304452
## + Fold04.Rep5: alpha=0.34217, lambda=3.683040
## - Fold04.Rep5: alpha=0.34217, lambda=3.683040
## + Fold04.Rep5: alpha=0.76305, lambda=0.037659
## - Fold04.Rep5: alpha=0.76305, lambda=0.037659
## + Fold04.Rep5: alpha=0.32620, lambda=0.010929
## - Fold04.Rep5: alpha=0.32620, lambda=0.010929
## + Fold04.Rep5: alpha=0.44663, lambda=0.001037
## - Fold04.Rep5: alpha=0.44663, lambda=0.001037
## + Fold04.Rep5: alpha=0.08757, lambda=0.012689
## - Fold04.Rep5: alpha=0.08757, lambda=0.012689
## + Fold04.Rep5: alpha=0.60040, lambda=0.003594
## - Fold04.Rep5: alpha=0.60040, lambda=0.003594
## + Fold04.Rep5: alpha=0.27368, lambda=0.453264
## - Fold04.Rep5: alpha=0.27368, lambda=0.453264
## + Fold04.Rep5: alpha=0.36848, lambda=4.961816
## - Fold04.Rep5: alpha=0.36848, lambda=4.961816
## + Fold05.Rep5: alpha=0.64457, lambda=0.002748
## - Fold05.Rep5: alpha=0.64457, lambda=0.002748
## + Fold05.Rep5: alpha=0.56029, lambda=0.304452
## - Fold05.Rep5: alpha=0.56029, lambda=0.304452
## + Fold05.Rep5: alpha=0.34217, lambda=3.683040
## - Fold05.Rep5: alpha=0.34217, lambda=3.683040
## + Fold05.Rep5: alpha=0.76305, lambda=0.037659
## - Fold05.Rep5: alpha=0.76305, lambda=0.037659
## + Fold05.Rep5: alpha=0.32620, lambda=0.010929
## - Fold05.Rep5: alpha=0.32620, lambda=0.010929
## + Fold05.Rep5: alpha=0.44663, lambda=0.001037
## - Fold05.Rep5: alpha=0.44663, lambda=0.001037
## + Fold05.Rep5: alpha=0.08757, lambda=0.012689
## - Fold05.Rep5: alpha=0.08757, lambda=0.012689
## + Fold05.Rep5: alpha=0.60040, lambda=0.003594
## - Fold05.Rep5: alpha=0.60040, lambda=0.003594
## + Fold05.Rep5: alpha=0.27368, lambda=0.453264
## - Fold05.Rep5: alpha=0.27368, lambda=0.453264
## + Fold05.Rep5: alpha=0.36848, lambda=4.961816
## - Fold05.Rep5: alpha=0.36848, lambda=4.961816
## + Fold06.Rep5: alpha=0.64457, lambda=0.002748
## - Fold06.Rep5: alpha=0.64457, lambda=0.002748
## + Fold06.Rep5: alpha=0.56029, lambda=0.304452
## - Fold06.Rep5: alpha=0.56029, lambda=0.304452
## + Fold06.Rep5: alpha=0.34217, lambda=3.683040
## - Fold06.Rep5: alpha=0.34217, lambda=3.683040
## + Fold06.Rep5: alpha=0.76305, lambda=0.037659
## - Fold06.Rep5: alpha=0.76305, lambda=0.037659
## + Fold06.Rep5: alpha=0.32620, lambda=0.010929
## - Fold06.Rep5: alpha=0.32620, lambda=0.010929
## + Fold06.Rep5: alpha=0.44663, lambda=0.001037
## - Fold06.Rep5: alpha=0.44663, lambda=0.001037
## + Fold06.Rep5: alpha=0.08757, lambda=0.012689
## - Fold06.Rep5: alpha=0.08757, lambda=0.012689
## + Fold06.Rep5: alpha=0.60040, lambda=0.003594
## - Fold06.Rep5: alpha=0.60040, lambda=0.003594
## + Fold06.Rep5: alpha=0.27368, lambda=0.453264
## - Fold06.Rep5: alpha=0.27368, lambda=0.453264
## + Fold06.Rep5: alpha=0.36848, lambda=4.961816
## - Fold06.Rep5: alpha=0.36848, lambda=4.961816
## + Fold07.Rep5: alpha=0.64457, lambda=0.002748
## - Fold07.Rep5: alpha=0.64457, lambda=0.002748
## + Fold07.Rep5: alpha=0.56029, lambda=0.304452
## - Fold07.Rep5: alpha=0.56029, lambda=0.304452
## + Fold07.Rep5: alpha=0.34217, lambda=3.683040
## - Fold07.Rep5: alpha=0.34217, lambda=3.683040
## + Fold07.Rep5: alpha=0.76305, lambda=0.037659
## - Fold07.Rep5: alpha=0.76305, lambda=0.037659
## + Fold07.Rep5: alpha=0.32620, lambda=0.010929
## - Fold07.Rep5: alpha=0.32620, lambda=0.010929
## + Fold07.Rep5: alpha=0.44663, lambda=0.001037
## - Fold07.Rep5: alpha=0.44663, lambda=0.001037
## + Fold07.Rep5: alpha=0.08757, lambda=0.012689
## - Fold07.Rep5: alpha=0.08757, lambda=0.012689
## + Fold07.Rep5: alpha=0.60040, lambda=0.003594
## - Fold07.Rep5: alpha=0.60040, lambda=0.003594
## + Fold07.Rep5: alpha=0.27368, lambda=0.453264
## - Fold07.Rep5: alpha=0.27368, lambda=0.453264
## + Fold07.Rep5: alpha=0.36848, lambda=4.961816
## - Fold07.Rep5: alpha=0.36848, lambda=4.961816
## + Fold08.Rep5: alpha=0.64457, lambda=0.002748
## - Fold08.Rep5: alpha=0.64457, lambda=0.002748
## + Fold08.Rep5: alpha=0.56029, lambda=0.304452
## - Fold08.Rep5: alpha=0.56029, lambda=0.304452
## + Fold08.Rep5: alpha=0.34217, lambda=3.683040
## - Fold08.Rep5: alpha=0.34217, lambda=3.683040
## + Fold08.Rep5: alpha=0.76305, lambda=0.037659
## - Fold08.Rep5: alpha=0.76305, lambda=0.037659
## + Fold08.Rep5: alpha=0.32620, lambda=0.010929
## - Fold08.Rep5: alpha=0.32620, lambda=0.010929
## + Fold08.Rep5: alpha=0.44663, lambda=0.001037
## - Fold08.Rep5: alpha=0.44663, lambda=0.001037
## + Fold08.Rep5: alpha=0.08757, lambda=0.012689
## - Fold08.Rep5: alpha=0.08757, lambda=0.012689
## + Fold08.Rep5: alpha=0.60040, lambda=0.003594
## - Fold08.Rep5: alpha=0.60040, lambda=0.003594
## + Fold08.Rep5: alpha=0.27368, lambda=0.453264
## - Fold08.Rep5: alpha=0.27368, lambda=0.453264
## + Fold08.Rep5: alpha=0.36848, lambda=4.961816
## - Fold08.Rep5: alpha=0.36848, lambda=4.961816
## + Fold09.Rep5: alpha=0.64457, lambda=0.002748
## - Fold09.Rep5: alpha=0.64457, lambda=0.002748
## + Fold09.Rep5: alpha=0.56029, lambda=0.304452
## - Fold09.Rep5: alpha=0.56029, lambda=0.304452
## + Fold09.Rep5: alpha=0.34217, lambda=3.683040
## - Fold09.Rep5: alpha=0.34217, lambda=3.683040
## + Fold09.Rep5: alpha=0.76305, lambda=0.037659
## - Fold09.Rep5: alpha=0.76305, lambda=0.037659
## + Fold09.Rep5: alpha=0.32620, lambda=0.010929
## - Fold09.Rep5: alpha=0.32620, lambda=0.010929
## + Fold09.Rep5: alpha=0.44663, lambda=0.001037
## - Fold09.Rep5: alpha=0.44663, lambda=0.001037
## + Fold09.Rep5: alpha=0.08757, lambda=0.012689
## - Fold09.Rep5: alpha=0.08757, lambda=0.012689
## + Fold09.Rep5: alpha=0.60040, lambda=0.003594
## - Fold09.Rep5: alpha=0.60040, lambda=0.003594
## + Fold09.Rep5: alpha=0.27368, lambda=0.453264
## - Fold09.Rep5: alpha=0.27368, lambda=0.453264
## + Fold09.Rep5: alpha=0.36848, lambda=4.961816
## - Fold09.Rep5: alpha=0.36848, lambda=4.961816
## + Fold10.Rep5: alpha=0.64457, lambda=0.002748
## - Fold10.Rep5: alpha=0.64457, lambda=0.002748
## + Fold10.Rep5: alpha=0.56029, lambda=0.304452
## - Fold10.Rep5: alpha=0.56029, lambda=0.304452
## + Fold10.Rep5: alpha=0.34217, lambda=3.683040
## - Fold10.Rep5: alpha=0.34217, lambda=3.683040
## + Fold10.Rep5: alpha=0.76305, lambda=0.037659
## - Fold10.Rep5: alpha=0.76305, lambda=0.037659
## + Fold10.Rep5: alpha=0.32620, lambda=0.010929
## - Fold10.Rep5: alpha=0.32620, lambda=0.010929
## + Fold10.Rep5: alpha=0.44663, lambda=0.001037
## - Fold10.Rep5: alpha=0.44663, lambda=0.001037
## + Fold10.Rep5: alpha=0.08757, lambda=0.012689
## - Fold10.Rep5: alpha=0.08757, lambda=0.012689
## + Fold10.Rep5: alpha=0.60040, lambda=0.003594
## - Fold10.Rep5: alpha=0.60040, lambda=0.003594
## + Fold10.Rep5: alpha=0.27368, lambda=0.453264
## - Fold10.Rep5: alpha=0.27368, lambda=0.453264
## + Fold10.Rep5: alpha=0.36848, lambda=4.961816
## - Fold10.Rep5: alpha=0.36848, lambda=4.961816
## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo, :
## There were missing values in resampled performance measures.
## Aggregating results
## Selecting tuning parameters
## Fitting alpha = 0.326, lambda = 0.0109 on full training set
# Best tuning parameter
elastic_reg$bestTune
## alpha lambda
## 3 0.3261968 0.01092878
# Make predictions on training set
predictions_train <- predict(elastic_reg, x)
eval_results(y_train, predictions_train, train)
## RMSE Rsquare
## 1 0.6505636 0.3448016
# Make predictions on test set
predictions_test <- predict(elastic_reg, x_test)
eval_results(y_test, predictions_test, test)
## RMSE Rsquare
## 1 0.6405588 0.3829841
colnames(df)
## [1] "fixed.acidity" "volatile.acidity" "citric.acid"
## [4] "residual.sugar" "chlorides" "free.sulfur.dioxide"
## [7] "total.sulfur.dioxide" "density" "pH"
## [10] "sulphates" "alcohol" "quality"
ggplot(data = df, mapping = aes(x = total.sulfur.dioxide, y = quality)) +
geom_point()
ggplot(data = df, mapping = aes(x = residual.sugar, y = quality)) +
geom_point()
There is really no relationship. This is probably an exercise in clusterting or machine learning, but linear regression is insufficient.
ggplot(data = df, mapping = aes(x = alcohol, y = quality)) +
geom_point() +
geom_smooth()
## `geom_smooth()` using method = 'gam' and formula 'y ~ s(x, bs = "cs")'